Why cats like to lick their own fur:
1. Cats are very clean animals and often groom themselves by licking their fur to remove dust and dirt.
2. In the hot summer, cats lick their fur to leave saliva on it, which helps them cool down. 
3. When cats feel anxious or uneasy, they will also lick their fur to relieve their emotions and release stress.
4. If a cat is infected with parasites, causing skin discomfort, it will lick the affected area incessantly. You should take the cat to a veterinary hospital for treatment as soon as possible.
5. If a cat is deficient in vitamins, it will supplement them by licking its fur. You may need to feed your cat pet trace element tablets.